Atomic excited states and the related energy levels

This article is about generalization and extension of the Bohr atomic model as well as the Rydberg formula to make them applicable to all atomic/ionic excited states and their energy levels. Bohr and Rydberg's original works were deemed only for hydrogen and the hydrogen-like ions but in time many mistakenly have come to the conclusion that those original forms of the theory are applicable to all species. This article clarifies the subject and helps with the misunderstandings. The article reviews first the original theory of atoms, the related excited states, and the related energy levels. It then shows the shortcoming of the original formulations and makes changes to generalize the theory and extend their applications to all atoms and their related ions. The theory of atomic excited states is re-formulated using a newly defined parameter called "characteristic exponent k" and the corresponding ionization energy. Numerical calculations and detailed works for several elements are presented to establish a better understanding of excited states. The article seeks also for a connection between the atomic energy levels and the internal structures and inner electrons of atoms. Furthermore, a small data bank is generated using the calculated "characteristic exponents k" for elements to be utilized for future simulations, studies, and research activities.